1. A justification for job training programs is that they improve worker productivity. Suppose that you are asked to evaluate whether more job training makes workers more productive. However, rather than having data on individual workers, you have access to data on manufacturing firms in Ohio. In particular, for each firm, you have information on hours of job training per worker (training) and the number of non-defective items produced per worker hour (output).

(i) Carefully state the ceteris paribus thought experiment underlying this policy question.

(ii) Does it seem likely that a firm’s decision to train its workers will be independent of worker characteristics? What are some of those measurable and unmeasurable worker characteristics? (iii) Name a factor other than worker characteristics that can affect worker productivity.

(iv) If you find a positive correlation between output and training, would you have convincingly established that job training makes workers more productive? Explain.

2. Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is

= 0 + 1 + ,

where is the unobserved error.

(i) What kinds of factors are contained in ? Are these likely to be correlated with the level of education?

(ii) Will a simple regression analysis uncover the ceteris paribus effect of education on fertility? Explain.

3. The data set BWGHT.RAW contains data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces ( ℎ ), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy ( ). The following simple regression was estimated using data on = 1,388 births,

bwght= 119.77 − 0.514

(i) What is the predicted birth weight when = 0? What about when = 20? Comment on the difference.

(ii) Does this simple regression necessarily capture a causal relationship between the child’s birth weight and the mother’s smoking habits? Explain.

(iii) To predict a birth weight of 125 ounces, what would have to be? Comment

4. Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and McClain (1995), the following equation relates housing price ( ) to the distance from a recently built garbage incinerator ( ):

log(price)= 9.40 + 0.312 log ( )

= 135, R^2 = 0.162

(i) Interpret the coefficient on log ( ). Is the sign of this estimate what you expect it to be?

(ii) Do you think simple regression provides an unbiased estimator of the ceteris paribus elasticity of price with respect to ? (Think about the city’s decision on where to put the incinerator.)

(iii) What other factors about a house affect its price? Might these be correlated with distance from the incinerator?

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